List questions from quadratic-residues

Published on 24 Jun 2015 - 15:35

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solve $x^2 \equiv 24 \pmod {60}$

Published on 24 Jun 2015 - 23:45

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Is there any simple trick to solve the congruence $a^{24}\equiv6a+2\pmod{13}$?

Published on 25 Jun 2015 - 7:23

115

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Show that $(r!)^2 ≡ (−1)^{r−1} \pmod p,\ r = (p-1)/2$

Published on 25 Mar 2026 - 23:38

362

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$r! \equiv (−1)^k \pmod p$

Published on 28 Mar 2026 - 2:48

63

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Find all values of $p$ such that $ax^2+bx+c \equiv 0 (\bmod p)$ have solution

Published on 28 Jun 2015 - 5:14

745

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Gauss' Lemma Proof Clarification

Published on 20 Jul 2015 - 1:46

127

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Literature on Quadratic Residues in Polynomial Quotient ring

Published on 21 Jul 2015 - 22:26

178

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Number of solutions to quadratic congruence

Published on 24 Jul 2015 - 15:21

511

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$2$-adic sequence converging to $\sqrt{-7}$.

Published on 29 Jul 2015 - 1:15

470

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Solving $x^2\equiv a\pmod{p}$ where $p\equiv5\pmod{8}$ and $a$ is a quadratic residue

Published on 05 Aug 2015 - 13:46

52

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How does this proof on quadratic congruences make sense?

Published on 11 Aug 2015 - 19:19

71

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Testing for quadratic residues

Published on 19 Aug 2015 - 2:32

163

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Solvability of $a \equiv x^2 \mod b$

Published on 22 Aug 2015 - 9:50

259

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Prove $8k+1$ is a quadratic residue mod $2^m$ for all $m\ge 1$.

Published on 13 Sep 2015 - 14:07

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Show how one can decrypt RSA message with e = 3 and $m<N^{1/3}$ without knowing the private key

solve $x^2 \equiv 24 \pmod {60}$

Is there any simple trick to solve the congruence $a^{24}\equiv6a+2\pmod{13}$?

Show that $(r!)^2 ≡ (−1)^{r−1} \pmod p,\ r = (p-1)/2$

$r! \equiv (−1)^k \pmod p$

Find all values of $p$ such that $ax^2+bx+c \equiv 0 (\bmod p)$ have solution

Gauss' Lemma Proof Clarification

Literature on Quadratic Residues in Polynomial Quotient ring

Number of solutions to quadratic congruence

$2$-adic sequence converging to $\sqrt{-7}$.

Solving $x^2\equiv a\pmod{p}$ where $p\equiv5\pmod{8}$ and $a$ is a quadratic residue

How does this proof on quadratic congruences make sense?

Testing for quadratic residues

Solvability of $a \equiv x^2 \mod b$

Prove $8k+1$ is a quadratic residue mod $2^m$ for all $m\ge 1$.

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